Low-Rank Tensor Train Coefficient Array Estimation for Tensor-on-Tensor Regression

doi:10.1109/TNNLS.2020.2967022

Low-Rank Tensor Train Coefficient Array Estimation for Tensor-on-Tensor Regression

2020-12-01

34

PRE

AI

DOI：10.1109/TNNLS.2020.2967022

Original

Original request for help

Save

Abstract

En 中文

The tensor-on-tensor regression can predict a tensor from a tensor, which generalizes most previous multilinear regression approaches, including methods to predict a scalar from a tensor, and a tensor from a scalar. However, the coefficient array could be much higher dimensional due to both high-order predictors and responses in this generalized way. Compared with the current low CANDECOMP/PARAFAC (CP) rank approximation-based method, the low tensor train (TT) approximation can further improve the stability and efficiency of the high or even ultrahigh-dimensional coefficient array estimation. In the proposed low TT rank coefficient array estimation for tensor-on-tensor regression, we adopt a TT rounding procedure to obtain adaptive ranks, instead of selecting ranks by experience. Besides, an l(2) constraint is imposed to avoid overfitting. The hierarchical alternating least square is used to solve the optimization problem. Numerical experiments on a synthetic data set and two real-life data sets demonstrate that the proposed method outperforms the state-of-the-art methods in terms of prediction accuracy with comparable computational complexity, and the proposed method is more computationally efficient when the data are high dimensional with small size in each mode.

Keywords:

Low-rank tensor train (TT)

motion capture

tensor regression

TT rounding

weather forecasting

Low-Rank Tensor Train Coefficient Array Estimation for Tensor-on-Tensor Regression

Abstract

AI Summary

Journal

Organization